The inner-outer gluing scheme has been a very
powerful tool in singularity formation problems for nonlinear elliptic and parabolic equations, see for instance [1]}, [2]}, [3]}. In those applications, the use of maximum principle is essential. In this paper we make the first attempt to extend this scheme to three-dimensional Euler flow and prove the Leapfrogging dynamics. We expect that this scheme will be a useful tool in studying finite time singularities or the Vortex Filament Conjecture for the incompressible Euler flow.
